ient Rule to differentiate the function. f(x) = x/ x^9+6

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=x^{2}…

A: The given function,  f(x) =x2e-x .........................(1)  differentiate with respect to x

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

A:

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: To find the antiderivative we integrate the given function c=integration constant

Q: Sketch the x^2 And the derivative And integration

A:

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

A:

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

A:

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

A:

Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: 2 - x f(x) = 3 x + 1

A: given that f(x)=2-x3x+1we need to find the derivative of the functionuse the quotient rule that is…

Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: 1 F(x) = -1. tanh 3x

A:

Q: what is the differentiate of f(x)=ln x

A:

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Differentiate the function   f(x) =    1/  ln x

A: Given function is fx=1lnx We know that 1an=a-n So, given function can be written as fx=lnx-1 Before…

Q: Calculate the derivative of f(x) = x^(1/ln(x)). What can be said about f(x) based on its derivative…

A: Consider the function,

Q: Determine the relative extrema of the function f (x) = = x' 3x² 24x + 32 using the second derivative…

A:

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

A:

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: sinx 3. f(x)=(x)*

A:

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given function is fx=1x+4. Compute the first derivative. f'x=1x+4'=-12x+432

Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A:

Q: Find y''by implicit differentiation. 2x3 + 5y3 = 2

A: We can find y" using implicit differentiation as below.

Q: Find relative extrema not using the first derivative test   s(x)=x^4-2x^2

A: We will use the second derivative test. But the route to second derivative passes through the first…

Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: What is the anti-differentiation rule to be used in order to integrate the function f Vx5 dx. a.…

A:

Q: Find the derivative of the function using chain rule. f(x) = esin?x

A:

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Using chain rule, find the derivative of the hyperbolic functions: f(x) = tanh(4x) f (x) = In…

A:

Q: Choose the rule that you would use to most efficiently find the derivative of the function 3 f(x) =…

A: The given function,   f(x)=32-x3 The general rule of differentiation is ddxxn=nxn-1

Q: Find the derivative of the function. g(x) = 2(3- Ex)

A:

Q: Differentiate the function. h(x) = ex9 + ln(x)

A:

Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: Applying natural logarithm on both sides, we get

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: Using the First Derivative Test, what are the local extrema for the function h(x) = 3x3 – 9x2 – 72x…

A: It is given that,              h(x)=3x3-9x2-72x+9we have to find the local extrema of the function.

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: Find the derivativeof ƒ(x) = x5. Then find the samederivative using the Product Rule withƒ(x) = x2…

A: We have to find the derivative of the function: fx=x5 We have to find same derivative with product…

Q: 13 Use the power rule to find the derivative of f(x) = 'Vx.

A:

Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: olve for the derivative of the function using chain rule.  2. f(x)=4√ -3x4-2

A: 2)

Q: Use product rule to find the derivative of f (x) = (x² + 5cosaæ)(x – 2x + tanx).

A: We can find the derivative of the given function using the product rule as below

Q: Use implicit differentiation by partial derivative to solve for dx of function 3x2 + 2xy = -4y3. %3D

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.